An online textbook/tutorial in elementary group theory. Group theory takes an abstract approach, dealing with many mathematical systems at once and requiring only that a mathematical system obey a few simple rules, seeking then to find properties common to all systems that obey these few rules. Contents include: What is Group Theory; Examples of Groups; Housekeeping Theorems; Cayley Tables; Subgroups; Cosets; Lagrange's Theorem; Cyclic Groups and Subgroups; and Permutations. From The Dog School of Mathematics.